{"id":"https://openalex.org/W4401439238","doi":"https://doi.org/10.1137/22m1515197","title":"Stochastic Mirror Descent for Convex Optimization with Consensus Constraints","display_name":"Stochastic Mirror Descent for Convex Optimization with Consensus Constraints","publication_year":2024,"publication_date":"2024-08-05","ids":{"openalex":"https://openalex.org/W4401439238","doi":"https://doi.org/10.1137/22m1515197"},"language":"en","primary_location":{"id":"doi:10.1137/22m1515197","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1515197","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033819196","display_name":"Anastasia Borovykh","orcid":"https://orcid.org/0000-0002-8550-4827"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A. Borovykh","raw_affiliation_strings":["Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031347000","display_name":"Nikolas Kantas","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"N. Kantas","raw_affiliation_strings":["Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083174192","display_name":"Panos Parpas","orcid":"https://orcid.org/0000-0002-2817-2301"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"P. Parpas","raw_affiliation_strings":["Department of Computing, Imperial College London, South Kensington Campus, SW7 2AZ, London"],"raw_orcid":"https://orcid.org/0000-0002-2817-2301","affiliations":[{"raw_affiliation_string":"Department of Computing, Imperial College London, South Kensington Campus, SW7 2AZ, London","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044857425","display_name":"Grigorios A. Pavliotis","orcid":"https://orcid.org/0000-0002-3468-9227"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"G. A. Pavliotis","raw_affiliation_strings":["Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London"],"raw_orcid":"https://orcid.org/0000-0002-3468-9227","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":0.4919,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71110301,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"23","issue":"3","first_page":"2208","last_page":"2241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6314884424209595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5508272647857666},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5026021003723145},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4785369336605072},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.47565099596977234},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.44618716835975647},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43350949883461},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42713814973831177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3993103504180908},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3587305545806885},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3566536605358124},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18250519037246704},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11284872889518738},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10736951231956482}],"concepts":[{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6314884424209595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5508272647857666},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5026021003723145},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4785369336605072},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.47565099596977234},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.44618716835975647},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43350949883461},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42713814973831177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3993103504180908},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3587305545806885},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3566536605358124},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18250519037246704},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11284872889518738},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10736951231956482},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1515197","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1515197","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1257954173","display_name":null,"funder_award_id":"EP/P031587/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1357342986","display_name":null,"funder_award_id":"EP/W003317/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2260019361","display_name":"ADOPT - Advancing optimisation technologies through international collaboration","funder_award_id":"EP/W003317/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4787172370","display_name":"Nonlocal Partial Differential Equations: entropies, gradient flows, phase transitions and applications","funder_award_id":"EP/P031587/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320307774","display_name":"JPMorgan Chase and Company","ror":"https://ror.org/01x3kkr08"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1569098853","https://openalex.org/W1571416372","https://openalex.org/W1935710009","https://openalex.org/W1964599043","https://openalex.org/W1995504856","https://openalex.org/W2001950057","https://openalex.org/W2004304255","https://openalex.org/W2021290840","https://openalex.org/W2055954415","https://openalex.org/W2060279450","https://openalex.org/W2066332749","https://openalex.org/W2148087609","https://openalex.org/W2164642931","https://openalex.org/W2266148951","https://openalex.org/W2517192452","https://openalex.org/W2535496140","https://openalex.org/W2551645646","https://openalex.org/W2731574071","https://openalex.org/W2763081248","https://openalex.org/W2763533254","https://openalex.org/W2901838001","https://openalex.org/W2940605178","https://openalex.org/W2963732316","https://openalex.org/W2964211247","https://openalex.org/W3011252985","https://openalex.org/W3042626397","https://openalex.org/W3092262213","https://openalex.org/W3100513551","https://openalex.org/W3101023041","https://openalex.org/W3108866329","https://openalex.org/W4206742934","https://openalex.org/W4248651508","https://openalex.org/W4292363360","https://openalex.org/W4301435544","https://openalex.org/W4312437966"],"related_works":["https://openalex.org/W2593225479","https://openalex.org/W2754965690","https://openalex.org/W4303684645","https://openalex.org/W2089887069","https://openalex.org/W2964170259","https://openalex.org/W3002546633","https://openalex.org/W159360277","https://openalex.org/W4206119629","https://openalex.org/W2765682467","https://openalex.org/W4382937879"],"abstract_inverted_index":{".The":[0],"mirror":[1,18,32,54,99,116,169],"descent":[2,55],"algorithm":[3,56,112],"is":[4,13,222],"known":[5],"to":[6,15,20,90,127,129],"be":[7],"effective":[8],"in":[9,57,101,216],"situations":[10],"where":[11,218],"it":[12],"beneficial":[14],"adapt":[16,128],"the":[17,21,25,29,35,70,74,84,96,119,131,134,138,141,153,173,176,181,185,192,195,209,219,226],"map":[19,117],"underlying":[22],"geometry":[23,36,132,139,221],"of":[24,31,37,69,76,98,110,133,140,165,175,184,194],"optimization":[26,39],"model.":[27],"However,":[28],"effect":[30,174],"maps":[33,100,170],"on":[34,180,197],"distributed":[38,53,103],"problems":[40,166],"has":[41],"not":[42,223],"been":[43],"previously":[44],"addressed.":[45],"In":[46],"this":[47],"paper":[48],"we":[49,105,167,190],"study":[50],"an":[51,114],"exact":[52],"continuous":[58],"time":[59],"under":[60],"additive":[61],"noise.":[62],"We":[63,144],"establish":[64,157],"a":[65,102,107,147],"linear":[66,159],"convergence":[67,160,182],"rate":[68,183],"proposed":[71,154,210],"dynamics":[72],"for":[73,152],"setting":[75,104],"convex":[77,198],"optimization.":[78],"Our":[79,205],"analysis":[80],"draws":[81],"motivation":[82],"from":[83],"augmented":[85],"Lagrangian":[86,120],"and":[87,137,156,202],"its":[88,158],"relation":[89],"gradient":[91],"tracking.":[92],"To":[93],"further":[94],"explore":[95],"benefits":[97],"present":[106],"preconditioned":[108],"variant":[109],"our":[111,125],"with":[113,201],"additional":[115],"over":[118],"dual":[121],"variables.":[122],"This":[123],"allows":[124],"method":[126,155,211],"both":[130,200],"primal":[135],"variables":[136],"consensus":[142],"constraint.":[143],"also":[145],"propose":[146],"Gauss\u2013Seidel":[148],"type":[149],"discretization":[150],"scheme":[151],"rate.":[161],"For":[162],"certain":[163],"classes":[164],"identify":[168],"that":[171,208],"mitigate":[172],"graph's":[177],"spectral":[178],"properties":[179],"algorithm.":[186],"Using":[187],"numerical":[188],"experiments,":[189],"demonstrate":[191],"efficiency":[193],"methodology":[196],"models,":[199],"without":[203],"constraints.":[204],"findings":[206],"show":[207],"outperforms":[212],"other":[213],"methods,":[214],"especially":[215],"scenarios":[217],"model's":[220],"captured":[224],"by":[225],"standard":[227],"Euclidean":[228],"norm.Keywordsdistributed":[229],"optimizationmirror":[230],"descentpreconditioninginteracting":[231],"particlesstochastic":[232],"optimizationMSC":[233],"codes65K1068Q8760G0768W15":[234]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}